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• Truth

Truth-perm-rev

Signature

(truth-perm-rev n perm truth numvars) → perm-truth

Arguments

n — current position in the list.
    Guard (natp n).

perm — indices to permute.
    Guard (index-listp perm numvars).

truth — truth table to permute.
    Guard (integerp truth).

numvars — Guard (natp numvars).

Returns

perm-truth — Type (integerp perm-truth).

Definitions and Theorems

Function: truth-perm-rev

(defun truth-perm-rev (n perm truth numvars)
       (declare (xargs :guard (and (natp n)
                                   (integerp truth)
                                   (natp numvars)
                                   (index-listp perm numvars))))
       (declare (xargs :guard (and (<= n numvars)
                                   (eql (len perm) numvars))))
       (let ((__function__ 'truth-perm-rev))
            (declare (ignorable __function__))
            (b* (((when (mbe :logic (zp (- (nfix numvars) (nfix n)))
                             :exec (eql n numvars)))
                  (truth-norm truth numvars))
                 (truth (truth-perm-rev (1+ (lnfix n))
                                        perm truth numvars)))
                (swap-vars n (nth n perm)
                           truth numvars))))

Theorem: integerp-of-truth-perm-rev

(defthm integerp-of-truth-perm-rev
        (b* ((perm-truth (truth-perm-rev n perm truth numvars)))
            (integerp perm-truth))
        :rule-classes :type-prescription)

Theorem: eval-of-truth-perm-rev-with-env-perm-rev

(defthm
   eval-of-truth-perm-rev-with-env-perm-rev
   (implies (index-listp perm numvars)
            (equal (truth-eval (truth-perm-rev n perm truth numvars)
                               (env-perm-rev n perm env numvars)
                               numvars)
                   (truth-eval truth env numvars))))

Theorem: eval-of-truth-perm-rev

(defthm
   eval-of-truth-perm-rev
   (implies (index-listp perm numvars)
            (equal (truth-eval (truth-perm-rev n perm truth numvars)
                               env numvars)
                   (truth-eval truth (env-perm n perm env numvars)
                               numvars))))

Theorem: size-of-truth-perm-rev-basic

(defthm size-of-truth-perm-rev-basic
        (b* ((?perm-truth (truth-perm-rev n perm truth numvars)))
            (implies (index-listp perm numvars)
                     (unsigned-byte-p (ash 1 (nfix numvars))
                                      perm-truth))))

Theorem: size-of-truth-perm-rev

(defthm size-of-truth-perm-rev
        (b* ((?perm-truth (truth-perm-rev n perm truth numvars)))
            (implies (and (natp size)
                          (<= (ash 1 (nfix numvars)) size)
                          (index-listp perm numvars))
                     (unsigned-byte-p size perm-truth))))

Theorem: truth-perm-rev-of-nfix-n

(defthm truth-perm-rev-of-nfix-n
        (equal (truth-perm-rev (nfix n)
                               perm truth numvars)
               (truth-perm-rev n perm truth numvars)))

Theorem: truth-perm-rev-nat-equiv-congruence-on-n

(defthm
     truth-perm-rev-nat-equiv-congruence-on-n
     (implies (nat-equiv n n-equiv)
              (equal (truth-perm-rev n perm truth numvars)
                     (truth-perm-rev n-equiv perm truth numvars)))
     :rule-classes :congruence)

Theorem: truth-perm-rev-of-ifix-truth

(defthm truth-perm-rev-of-ifix-truth
        (equal (truth-perm-rev n perm (ifix truth)
                               numvars)
               (truth-perm-rev n perm truth numvars)))

Theorem: truth-perm-rev-int-equiv-congruence-on-truth

(defthm
     truth-perm-rev-int-equiv-congruence-on-truth
     (implies (int-equiv truth truth-equiv)
              (equal (truth-perm-rev n perm truth numvars)
                     (truth-perm-rev n perm truth-equiv numvars)))
     :rule-classes :congruence)

Theorem: truth-perm-rev-of-nfix-numvars

(defthm truth-perm-rev-of-nfix-numvars
        (equal (truth-perm-rev n perm truth (nfix numvars))
               (truth-perm-rev n perm truth numvars)))

Theorem: truth-perm-rev-nat-equiv-congruence-on-numvars

(defthm
     truth-perm-rev-nat-equiv-congruence-on-numvars
     (implies (nat-equiv numvars numvars-equiv)
              (equal (truth-perm-rev n perm truth numvars)
                     (truth-perm-rev n perm truth numvars-equiv)))
     :rule-classes :congruence)